Time dummies or Time trend?

[karamat khan]

Hello everyone
I have a question about time dummies and time trend, I hope someone can help.
I have panel data set consists of T=27 and N=42
I am using fixed effects, random effects, ivreg2 with and without cluster errors.
Here “X” is my main explanatory variable and rest are controls. As I use only country dummies with other control variables then results are significantly negative (which is favorable), but when I also add time dummies then coefficients on my main variable becomes insignificant, yet using time-trend dummy with country dummies again provide favorable results.
I have used alternates for both dependent variable and my main explanatory variable but found similar pattern of results. My question is, can I use time trend as an alternate to time-dummies? I have searched for literature in similar topic area and found that they have either used time dummies or country dummies or even some of them did not used both time and country dummies, I did not found any paper (in similar area) where they have used both time and country dummies simultaneously. would it be reasonable to proceed with results obtained from only country dummies or with country dummies and time-trend?
Thanks a lot!


Results estimation with country dummies

 

(1)
(2)
(3)
(4)


Fixed effects
Random effects
IVREG2
IVREG2(cluster err.)

X
-0.013***
-0.013***
-0.064***
-0.064***


(0.0021)
(0.0021)
(0.0058)
(0.0188)

lnpn_w
0.618***
0.618***
0.723***
0.723***


(0.0208)
(0.0208)
(0.0276)
(0.1127)

pse_w
-0.013***
-0.013***
-0.013***
-0.013***


(0.0008)
(0.0008)
(0.0010)
(0.0035)

religion
0.000
-1.013***
-1.060***
-1.060**


(0.0000)
(0.1503)
(0.1835)
(0.4129)

L.polity2
-0.014***
-0.014***
-0.017***
-0.017


(0.0041)
(0.0041)
(0.0050)
(0.0123)

L.gdpg_w
-0.004
-0.004
-0.006*
-0.006


(0.0027)
(0.0027)
(0.0033)
(0.0042)

popd_w
-0.002***
-0.002***
0.003***
0.003


(0.0006)
(0.0006)
(0.0009)
(0.0036)

indep

0.012
0.044***
0.044***



(0.0072)
(0.0094)
(0.0134)

2.colonyg

-0.595***
1.360***
1.360



(0.1984)
(0.3138)
(1.0563)

3.colonyg

-0.515**
0.813**
0.813



(0.2484)
(0.3321)
(1.1266)

4.colonyg

-1.044***
1.011***
1.011



(0.2528)
(0.3730)
(1.1353)

5.colonyg

-0.959***
0.320
0.320



(0.2522)
(0.3344)
(1.1388)

6.colonyg

-1.616***
0.078
0.078



(0.2307)
(0.3305)
(1.2015)

2.ccode

-0.526***
-1.158***
-1.158***



(0.1711)
(0.2185)
(0.3720)

3.ccode

-0.283**
0.506***
0.506



(0.1128)
(0.1595)
(0.3354)

4.ccode

-0.582***
-0.672***
-0.672



(0.2020)
(0.2468)
(0.5241)

5.ccode

-1.148***
-0.650***
-0.650**



(0.1197)
(0.1548)
(0.2894)

6.ccode

-0.677***
0.779***
0.779



(0.1632)
(0.2485)
(0.6407)

7.ccode

0.119
-0.306**
-0.306



(0.1192)
(0.1519)
(0.2231)

8.ccode

-1.126***
-1.469***
-1.469***



(0.1260)
(0.1578)
(0.2405)

9.ccode

0.047
-0.357
-0.357



(0.2101)
(0.2597)
(0.5217)

10.ccode

-1.885***
-2.900***
-2.900***



(0.2793)
(0.3564)
(0.8709)

11.ccode

-1.180***
-0.036
-0.036



(0.2259)
(0.2995)
(1.0262)

12.ccode

-0.224
-0.540**
-0.540



(0.1957)
(0.2411)
(0.6245)

13.ccode

-0.240**
-0.386***
-0.386



(0.1218)
(0.1494)
(0.2503)

15.ccode

-0.134
0.144
0.144



(0.1187)
(0.1477)
(0.2148)

17.ccode

-0.625***
-0.634***
-0.634



(0.1276)
(0.1557)
(0.3943)

18.ccode

-0.174
-0.474***
-0.474*



(0.1220)
(0.1520)
(0.2539)

19.ccode

-0.135
-0.049
-0.049



(0.1497)
(0.1829)
(0.2412)

20.ccode

0.141
-0.271
-0.271



(0.1916)
(0.2376)
(0.4312)

21.ccode

-0.631***
-0.768***
-0.768***



(0.1173)
(0.1439)
(0.2395)

22.ccode

0.622***
1.249***
1.249***



(0.1174)
(0.1569)
(0.2829)

23.ccode

0.189*
0.317**
0.317



(0.1114)
(0.1366)
(0.2080)

24.ccode

-0.225*
-0.243
-0.243



(0.1288)
(0.1572)
(0.3998)

25.ccode

0.769***
0.127
0.127



(0.1293)
(0.1709)
(0.4158)

26.ccode

0.249
0.449*
0.449



(0.2107)
(0.2581)
(0.5582)

27.ccode

-2.795***
-1.676***
-1.676**



(0.1507)
(0.2165)
(0.6721)

28.ccode

0.138
0.632
0.632



(0.4002)
(0.4911)
(1.6173)

29.ccode

0.941***
0.926***
0.926***



(0.1174)
(0.1433)
(0.2457)

30.ccode

-0.027
1.241***
1.241**



(0.1820)
(0.2571)
(0.6151)

31.ccode

-0.612***
-0.707***
-0.707



(0.2067)
(0.2525)
(0.4854)

32.ccode

2.086***
1.563***
1.563**



(0.1497)
(0.1904)
(0.6354)

34.ccode

-3.169***
-2.065***
-2.065**



(0.2357)
(0.3090)
(0.9537)

35.ccode

0.192
0.349
0.349



(0.1912)
(0.2340)
(0.4164)

37.ccode

1.548***
3.249***
3.249***



(0.2013)
(0.3008)
(0.7142)

39.ccode

-0.082
-0.141
-0.141



(0.1302)
(0.1590)
(0.1996)

41.ccode

0.465***
-0.115
-0.115



(0.1445)
(0.1861)
(0.4616)

_cons
3.719***
4.015***
-0.407
-0.407


(0.2201)
(0.5093)
(0.7682)
(1.9079)

N
1134
1134
1134
1134

r2
0.494

0.968
0.968

r2_a
0.47

0.97
0.97

Results estimation with time and country dummies

 

(1)
(2)
(3)
(4)


Fixed effects
Random effects
IVREG2
IVREG2(cluster err.)

X
0.001
0.001
0.012
0.012


(0.0020)
(0.0020)
(0.0145)
(0.0468)

lnpn_w
0.828***
0.828***
0.818***
0.818***


(0.0222)
(0.0222)
(0.0258)
(0.0993)

pse_w
-0.007***
-0.007***
-0.006***
-0.006*


(0.0008)
(0.0008)
(0.0012)
(0.0036)

religion
0.000
-0.265*
-0.234*
-0.234


(0.0000)
(0.1371)
(0.1402)
(0.3485)

L.polity2
0.007**
0.007**
0.009**
0.009


(0.0037)
(0.0037)
(0.0043)
(0.0111)

L.gdpg_w
-0.002
-0.002
-0.002
-0.002


(0.0024)
(0.0024)
(0.0023)
(0.0028)

popd_w
0.002***
0.002***
0.002**
0.002


(0.0006)
(0.0006)
(0.0008)
(0.0040)

indep

-0.004
-0.012
-0.012



(0.0062)
(0.0119)
(0.0315)

1992.year
-0.077
-0.077
-0.077
-0.077***


(0.0732)
(0.0732)
(0.0719)
(0.0288)

1993.year
-0.146**
-0.146**
-0.145**
-0.145***


(0.0743)
(0.0743)
(0.0730)
(0.0479)

1994.year
-0.206***
-0.206***
-0.201***
-0.201***


(0.0754)
(0.0754)
(0.0743)
(0.0641)

1995.year
-0.244***
-0.244***
-0.238***
-0.238***


(0.0763)
(0.0763)
(0.0754)
(0.0769)

1996.year
-0.291***
-0.291***
-0.276***
-0.276**


(0.0775)
(0.0775)
(0.0783)
(0.1084)

1997.year
-0.332***
-0.332***
-0.325***
-0.325***


(0.0785)
(0.0785)
(0.0777)
(0.1061)

1998.year
-0.395***
-0.395***
-0.391***
-0.391***


(0.0792)
(0.0792)
(0.0779)
(0.1109)

1999.year
-0.462***
-0.462***
-0.458***
-0.458***


(0.0800)
(0.0800)
(0.0787)
(0.1256)

2000.year
-0.496***
-0.496***
-0.494***
-0.494***


(0.0811)
(0.0811)
(0.0796)
(0.1330)

2001.year
-0.538***
-0.538***
-0.538***
-0.538***


(0.0822)
(0.0822)
(0.0807)
(0.1377)

2002.year
-0.607***
-0.607***
-0.620***
-0.620***


(0.0834)
(0.0834)
(0.0834)
(0.1417)

2003.year
-0.700***
-0.700***
-0.717***
-0.717***


(0.0845)
(0.0845)
(0.0858)
(0.1515)

2004.year
-0.779***
-0.779***
-0.787***
-0.787***


(0.0849)
(0.0849)
(0.0839)
(0.1656)

2005.year
-0.842***
-0.842***
-0.854***
-0.854***


(0.0859)
(0.0859)
(0.0857)
(0.1691)

2006.year
-0.881***
-0.881***
-0.899***
-0.899***


(0.0865)
(0.0865)
(0.0878)
(0.1689)

2007.year
-0.928***
-0.928***
-0.961***
-0.961***


(0.0873)
(0.0873)
(0.0957)
(0.1781)

2008.year
-0.988***
-0.988***
-1.035***
-1.035***


(0.0880)
(0.0880)
(0.1053)
(0.2027)

2009.year
-1.051***
-1.051***
-1.109***
-1.109***


(0.0883)
(0.0883)
(0.1140)
(0.2317)

2010.year
-1.101***
-1.101***
-1.163***
-1.163***


(0.0886)
(0.0886)
(0.1181)
(0.2455)

2011.year
-1.114***
-1.114***
-1.188***
-1.188***


(0.0899)
(0.0899)
(0.1292)
(0.2804)

2012.year
-1.138***
-1.138***
-1.219***
-1.219***


(0.0907)
(0.0907)
(0.1368)
(0.3047)

2013.year
-1.164***
-1.164***
-1.252***
-1.252***


(0.0911)
(0.0911)
(0.1442)
(0.3287)

2014.year
-1.200***
-1.200***
-1.294***
-1.294***


(0.0919)
(0.0919)
(0.1505)
(0.3496)

2015.year
-1.242***
-1.242***
-1.346***
-1.346***


(0.0929)
(0.0929)
(0.1618)
(0.3858)

2016.year
-1.290***
-1.290***
-1.389***
-1.389***


(0.0933)
(0.0933)
(0.1569)
(0.3697)

2017.year
-1.352***
-1.352***
-1.441***
-1.441***


(0.0934)
(0.0934)
(0.1467)
(0.3365)

2.colonyg

0.501***
0.247
0.247



(0.1759)
(0.3683)
(1.4945)

3.colonyg

0.755***
0.679***
0.679



(0.2207)
(0.2375)
(1.1131)

4.colonyg

-0.255
-0.528
-0.528



(0.2173)
(0.4110)
(1.5514)

5.colonyg

1.177***
1.166***
1.166



(0.2362)
(0.2322)
(1.0290)

6.colonyg

0.757***
0.666***
0.666



(0.2254)
(0.2503)
(1.2043)

2.ccode

0.076
0.262
0.262



(0.1481)
(0.2795)
(0.7095)

3.ccode

-0.250***
-0.409*
-0.409



(0.0966)
(0.2247)
(0.7145)

4.ccode

-0.731***
-0.665***
-0.665



(0.1781)
(0.1948)
(0.4904)

5.ccode

-0.817***
-0.874***
-0.874**



(0.1025)
(0.1242)
(0.3553)

6.ccode

-1.314***
-1.690***
-1.690



(0.1470)
(0.5042)
(1.5754)

7.ccode

0.474***
0.609***
0.609



(0.1038)
(0.2007)
(0.5474)

8.ccode

-0.344***
-0.185
-0.185



(0.1140)
(0.2327)
(0.6072)

9.ccode

0.228
0.388
0.388



(0.1854)
(0.2739)
(0.7441)

10.ccode

-1.723***
-1.560***
-1.560*



(0.2378)
(0.3132)
(0.9248)

11.ccode

0.434**
0.411**
0.411



(0.2067)
(0.2049)
(0.9647)

12.ccode

0.710***
0.842***
0.842



(0.1719)
(0.2398)
(0.5624)

13.ccode

-0.118
-0.052
-0.052



(0.1054)
(0.1336)
(0.3153)

15.ccode

0.222**
0.166
0.166



(0.1066)
(0.1268)
(0.2893)

17.ccode

0.073
0.138
0.138



(0.1131)
(0.1385)
(0.3430)

18.ccode

-0.274***
-0.244**
-0.244



(0.1037)
(0.1092)
(0.2738)

19.ccode

-0.365***
-0.425***
-0.425



(0.1281)
(0.1476)
(0.2907)

20.ccode

0.282*
0.429*
0.429



(0.1683)
(0.2510)
(0.6651)

21.ccode

-0.560***
-0.545***
-0.545***



(0.0999)
(0.1001)
(0.1767)

22.ccode

0.032
-0.146
-0.146



(0.1032)
(0.2494)
(0.6940)

23.ccode

0.086
0.032
0.032



(0.0957)
(0.1171)
(0.2659)

24.ccode

0.482***
0.545***
0.545*



(0.1142)
(0.1385)
(0.3048)

25.ccode

-0.028
0.006
0.006



(0.1156)
(0.1217)
(0.4222)

26.ccode

0.239
0.266
0.266



(0.1848)
(0.1846)
(0.4793)

27.ccode

-1.159***
-1.258***
-1.258*



(0.1547)
(0.1980)
(0.7526)

28.ccode

-1.893***
-2.307***
-2.307



(0.3651)
(0.6419)
(2.0185)

29.ccode

0.165
0.123
0.123



(0.1085)
(0.1190)
(0.2280)

30.ccode

0.159
-0.078
-0.078



(0.1557)
(0.3404)
(1.1152)

31.ccode

-0.281
-0.171
-0.171



(0.1816)
(0.2271)
(0.5612)

32.ccode

0.502***
0.495***
0.495



(0.1523)
(0.1497)
(0.4660)

34.ccode

-2.716***
-2.986***
-2.986**



(0.2187)
(0.4077)
(1.3239)

35.ccode

0.035
0.042
0.042



(0.1665)
(0.1637)
(0.3526)

37.ccode

0.708***
0.323
0.323



(0.1752)
(0.5241)
(1.6380)

39.ccode

-0.193*
-0.195*
-0.195



(0.1102)
(0.1082)
(0.1289)

41.ccode

-0.141
-0.102
-0.102



(0.1257)
(0.1331)
(0.4565)

_cons
0.794***
0.709
1.309
1.309


(0.2426)
(0.4683)
(0.8978)
(3.1182)

N
1134
1134
1134
1134

r2
0.647

0.985
0.985

r2_a
0.62

0.98
0.98

Results Estimation with Time trend and country dummies

  

(1)
(2)
(3)
(4)


Fixed effects
Random effects
IVREG2
IVREG2(cluster err.)

X
-0.004*
-0.004*
-0.038***
-0.038*


(0.0020)
(0.0020)
(0.0075)
(0.0208)

lnpn_w
0.671***
0.671***
0.712***
0.712***


(0.0195)
(0.0195)
(0.0230)
(0.0897)

pse_w
-0.010***
-0.010***
-0.011***
-0.011***


(0.0008)
(0.0008)
(0.0010)
(0.0029)

religion
0.000
-0.826***
-0.929***
-0.929**


(0.0000)
(0.1389)
(0.1539)
(0.3698)

L.polity2
-0.007*
-0.007*
-0.011***
-0.011


(0.0038)
(0.0038)
(0.0043)
(0.0097)

L.gdpg_w
-0.003
-0.003
-0.005*
-0.005


(0.0025)
(0.0025)
(0.0028)
(0.0035)

popd_w
-0.000
-0.000
0.002**
0.002


(0.0006)
(0.0006)
(0.0008)
(0.0035)

indep

0.001
0.024***
0.024*



(0.0067)
(0.0088)
(0.0148)

Time trend dummy
-0.446***
-0.446***
-0.266***
-0.266***


(0.0317)
(0.0317)
(0.0512)
(0.1023)

2.colonyg

-0.135
0.831***
0.831



(0.1855)
(0.2867)
(1.0396)

3.colonyg

0.219
0.705**
0.705



(0.2344)
(0.2765)
(1.0840)

4.colonyg

-0.607***
0.427
0.427



(0.2346)
(0.3361)
(1.1372)

5.colonyg

0.093
0.422
0.422



(0.2438)
(0.2762)
(1.0750)

6.colonyg

-0.572**
0.005
0.005



(0.2249)
(0.2746)
(1.1259)

2.ccode

-0.172
-0.687***
-0.687*



(0.1594)
(0.2054)
(0.3829)

3.ccode

-0.359***
0.137
0.137



(0.1039)
(0.1541)
(0.3210)

4.ccode

-0.398**
-0.525**
-0.525



(0.1863)
(0.2062)
(0.4466)

5.ccode

-0.974***
-0.750***
-0.750***



(0.1109)
(0.1303)
(0.2654)

6.ccode

-1.209***
-0.136
-0.136



(0.1548)
(0.2812)
(0.6198)

7.ccode

0.389***
0.029
0.029



(0.1114)
(0.1434)
(0.2223)

8.ccode

-0.648***
-1.043***
-1.043***



(0.1208)
(0.1562)
(0.2652)

9.ccode

0.397**
0.018
0.018



(0.1949)
(0.2280)
(0.4679)

10.ccode

-1.925***
-2.507***
-2.507***



(0.2570)
(0.3071)
(0.8275)

11.ccode

-0.317
0.009
0.009



(0.2167)
(0.2474)
(0.9913)

12.ccode

0.149
-0.188
-0.188



(0.1820)
(0.2117)
(0.5493)

13.ccode

-0.054
-0.215*
-0.215



(0.1128)
(0.1283)
(0.2028)

15.ccode

-0.122
0.037
0.037



(0.1093)
(0.1244)
(0.1798)

17.ccode

-0.330***
-0.454***
-0.454



(0.1192)
(0.1334)
(0.3566)

18.ccode

-0.264**
-0.405***
-0.405*



(0.1124)
(0.1268)
(0.2462)

19.ccode

-0.322**
-0.196
-0.196



(0.1384)
(0.1541)
(0.2312)

20.ccode

0.440**
0.076
0.076



(0.1775)
(0.2091)
(0.3849)

21.ccode

-0.656***
-0.727***
-0.727***



(0.1079)
(0.1193)
(0.2092)

22.ccode

0.309***
0.805***
0.805**



(0.1103)
(0.1593)
(0.3147)

23.ccode

0.051
0.182
0.182



(0.1030)
(0.1162)
(0.1748)

24.ccode

0.074
-0.057
-0.057



(0.1204)
(0.1349)
(0.3463)

25.ccode

0.367***
0.151
0.151



(0.1224)
(0.1417)
(0.3966)

26.ccode

0.486**
0.508**
0.508



(0.1946)
(0.2136)
(0.5079)

27.ccode

-2.225***
-1.796***
-1.796***



(0.1444)
(0.1821)
(0.5761)

28.ccode

-1.286***
-0.420
-0.420



(0.3818)
(0.4563)
(1.5422)

29.ccode

0.684***
0.779***
0.779***



(0.1095)
(0.1218)
(0.2174)

30.ccode

-0.064
0.698***
0.698



(0.1675)
(0.2431)
(0.5562)

31.ccode

-0.210
-0.429**
-0.429



(0.1923)
(0.2159)
(0.4373)

32.ccode

1.527***
1.445***
1.445***



(0.1433)
(0.1582)
(0.5266)

34.ccode

-3.406***
-2.660***
-2.660***



(0.2175)
(0.2851)
(0.7795)

35.ccode

0.307*
0.353*
0.353



(0.1761)
(0.1935)
(0.3771)

37.ccode

1.137***
2.305***
2.305***



(0.1875)
(0.3192)
(0.7490)

39.ccode

-0.133
-0.148
-0.148



(0.1198)
(0.1315)
(0.1643)

41.ccode

0.155
-0.062
-0.062



(0.1348)
(0.1547)
(0.4277)

_cons
2.591***
2.907***
0.748
0.748


(0.2178)
(0.4751)
(0.6893)
(1.8020)

N
1134
1134
1134
1134

r2
0.572

0.978
0.978

r2_a
0.55

0.98
0.98

[Clyde Schechter]

My question is, can I use time trend as an alternate to time-dummies?

No, you can't.

You need to consider the real world data-generating process and pick the one that is correct. (Well, actually you can use time-indicators ("dummies"), as an alternate to trend, but not the other way around. If a time trend is appropriate, time indicators will capture it correctly, although it will be difficult to see that in the results.) A time trend variable would be a correct specification only for a process where, in the real world, the outcome variable tends to increase (or decrease as the case may be) by approximately the same amount each time period. It is a very specific and strict assumption to use a time trend. By contrast, time indicators can be used to specify any kind of time-variation in the outcome variable: it can go up in some periods and down in others, and the amounts can vary in any arbitrary way.

So, in the end, this is not a statistical question, it's a question in your science domain. It appears that your review of the literature, at least so far, has not given you a clear answer to this question. You might want to discuss this with other experts in your field.

[karamat khan]

I am really grateful for your kind reply sir, one related question, may i use vce(cluster year) instead of country or region?

[Clyde Schechter]

It is perfectly legal in Stata to do that. But I have never seen it done and it is difficult for me to imagine a situation where that would be appropriate. The purpose of using the cluster-robust variance estimator is to account for the non-independence of observations within the clusters. Thus you can expect that a given country or region's attributes might tend to remain more similar over time than their resemblance to other countries. Sometimes there is even explicit autocorrelation. But in general one doesn't expect the resemblance of different countries' attributes to be more similar in one year than over several years. When there is good reason to expect that, then it might make sense to use clustering of both years and country or region; the -reghdfe- command by Sergio Correa, available from SSC, can do that.

Again, though, this really depends on your understanding of the real world data generating process. The clustering specified in the commands should reflect the real-world clustering.